Which type of sorting is used in the std::sort()?

GCC 9.2.0 libstdc++ source confirming introsort

Others have mentioned introsort, but here is some evidence for libstc++, which is the default C++ implementation on most Linux distros.

libstdc++ is a part of GCC itself, so we will look into GCC source.

libstdc++-v3/include/std/algorithm is the main header and contains:

#include <bits/stl_algobase.h>
#include <bits/stl_algo.h>

Then, bits/stl_algo.h contains the definition of the sort overloads, one of them being:

  /**
   *  @brief Sort the elements of a sequence.
   *  @ingroup sorting_algorithms
   *  @param  __first   An iterator.
   *  @param  __last    Another iterator.
   *  @return  Nothing.
   *
   *  Sorts the elements in the range @p [__first,__last) in ascending order,
   *  such that for each iterator @e i in the range @p [__first,__last-1),  
   *  *(i+1)<*i is false.
   *
   *  The relative ordering of equivalent elements is not preserved, use
   *  @p stable_sort() if this is needed.
  */
  template<typename _RandomAccessIterator>
    inline void
    sort(_RandomAccessIterator __first, _RandomAccessIterator __last)
    {
      // concept requirements
      __glibcxx_function_requires(_Mutable_RandomAccessIteratorConcept<
        _RandomAccessIterator>)
      __glibcxx_function_requires(_LessThanComparableConcept<
        typename iterator_traits<_RandomAccessIterator>::value_type>)
      __glibcxx_requires_valid_range(__first, __last);
      __glibcxx_requires_irreflexive(__first, __last);

      std::__sort(__first, __last, __gnu_cxx::__ops::__iter_less_iter());
    }

so we see that this just does a bunch of sanity checks on the input, and then calls std::__sort which is defined in the same file:

  template<typename _RandomAccessIterator, typename _Compare>
    inline void
    __sort(_RandomAccessIterator __first, _RandomAccessIterator __last,
       _Compare __comp)
    {
      if (__first != __last)
    {
      std::__introsort_loop(__first, __last,
                std::__lg(__last - __first) * 2,
                __comp);
      std::__final_insertion_sort(__first, __last, __comp);
    }
    }

and I'll stop here that we have reached an identifier called std::__introsort_loop, the rest of the implementation is on the same file is anyone still has doubts.

It should also be possible to GDB step debug into std::sort without any further setup in Ubuntu 18.04 as mentioned for std::set at: What is the underlying data structure of a STL set in C++?

C++17 parallel sorting

We now also have parallel sorting, so it would be worth looking on how it is done as well: Are C++17 Parallel Algorithms implemented already?

As mentioned in the above answer, the implementation relies on an external library: Intel Thread Building Blocks: https://github.com/intel/tbb